Answered

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A scoop of ice cream is in the shape of a perfect sphere and it sits on top of a cone. The diameter of the sphere equals the diameter of the base of the cone, which is 8 cm. How tall must the cone be so that if the ice cream melts, it will all fit into the cone

Sagot :

Answer:

(At least) 10 centimeters.

Step-by-step explanation:

The radius of the ice cream scoop is 2.5 cm and the radius of the cone is also 2.5 cm.

We want to determine the height of the cone such that it will fit all of the ice cream when it melts without any spilling.

First, we will find the volume of the ice cream scoop. The volume for a sphere is given by:

Since the radius is 2.5 cm, the volume of the full ice cream scoop is:

The volume of a cone is given by:

The radius of the cone is 2.5 cm. Therefore:

The volume of the cone should be equal to the volume of the scoop. So.

The height of the cone should be (at least) 10 cm.

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